Graph coloring | Theorems in graph theory
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color. The five color theorem is implied by the stronger four color theorem, but is considerably easier to prove. It was based on a failed attempt at the four color proof by Alfred Kempe in 1879. Percy John Heawood found an error 11 years later, and proved the five color theorem based on Kempe's work. (Wikipedia).
Proof: The Angle Bisector Theorem
This video states and proves the angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Relationships with Triangles
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From playlist Shorts
Upper and Lower Bounds for the Chromatic Number of a Graph
This video explains how to determine the upper and lower bounds of the chromatic number to various graphs. Then the chromatic number is found. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Determine Which Graphs have a Given Chromatic Number
This video explains how to determine which special graphs have a chromatic number of 6. mathispower4u.com
From playlist Graph Theory (Discrete Math)
4-Colorabiity - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Calculus 3: Green's Theorem (17 of 21) More Examples 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will show why Green's Theorem is the best method to solve this problem. Next video in the series can be seen at: https://youtu.be/suVcTxD9lYw
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM
Applying and understanding the addition rule of probability.
From playlist Unit 5 Probability A: Basic Probability
Geometry - Ch. 1: Basic Concepts (26 of 49) Congruent Sides and Congruent Angles: Ex.
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how to identify quadrilaterals, triangles that are equilateral triangles, quadrilaterals that are also a square by by observing the angles, sides, and their congruences of the figures. Next v
From playlist GEOMETRY CH 1 BASIC CONCEPTS
The Four Color Theorem - What Counts as a Proof?
Train your problem solving skills today with SkillShare: https://skl.sh/upandatom3 Check out the video we did over on Willie's Channel! https://youtu.be/jwQlULjESTs Subscribe to Willie's Channel KhAnubis! https://www.youtube.com/user/tobirates The Four Color Map Theorem and why it was
From playlist Math
The Five Color Theorem (without Kempe chains)
Submission for the #SoME2 competition. Most animations were done in manim (https://www.manim.community/), and the 3d images were rendered using svg3d (https://github.com/prideout/svg3d). Proofs: The degree of a vertex or a face is the number of edge incidences (edges that meet a vertex o
From playlist Summer of Math Exposition 2 videos
Louis Esperet: Coloring graphs on surfaces
Recording during the thematic meeting: "Graphs and surfaces: algorithms, combinatorics and topology" the May 11, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematici
From playlist Mathematical Aspects of Computer Science
AlgTop10: More on graphs and Euler's formula
We discuss applications of Euler's formula to various planar situations, in particular to planar graphs, including complete and complete bipartite graphs, the Five neighbours theorem, the Six colouring theorem, and to Pick's formula, which lets us compute the area of an integral polygonal
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Graph list-coloring and Thomassen's theorem #SoME2
Some videos on topics that appear on the video: Induction: https://www.youtube.com/watch?v=5Hn8vUE3cBQ Planar graphs & four color theorem: https://www.youtube.com/watch?v=xBkTIp6ajAg https://www.youtube.com/watch?v=NgbK43jB4rQ Image credit: Francis Guthrie: Unknown author, Public domain,
From playlist Summer of Math Exposition 2 videos
Susan Goldstine - Maps of Strange Worlds: Beyond the Four-Color Theorem - CoM Jan 2021
In 1852, a math student posed a deceptively simple-sounding question: if you want to color a map so that bordering regions always have different colors, how many colors do you need? This opened a rabbit hole that has kept mathematicians, computer scientists, and philosophers occupied for
From playlist Celebration of Mind 2021
William Gasarch - Rectangle Free Colorings- G4G12 April 2016
An nxm grid is c-colorable if you can c-color it without any rectangles having all four points the same color. We discuss which grids are 2,3, and 4 colorable.
From playlist G4G12 Videos
Francisco Martinez Figueroa (8/19/22): Chromatic number of G-Borsuk graphs
The Borsuk graph has vertex set the sphere S^d, and edges x∼y whenever x and y are ϵ-almost antipodal. It is well known that when epsilon is small, its chromatic number is d+2, which follows from the topology of S^d via Borsuk-Ulam's Theorem. Given a finite group G acting freely over a com
From playlist Vietoris-Rips Seminar
Here's a very nice Martin Gardner problem. Take four color pencils and try! The picture can be downloaded here: hhttps://drive.google.com/file/d/1eM1t_bTU016YxsMa6tahVsO1pHVfaHu9/view?usp=sharing Next puzzle: http://www.youtube.com/watch?v=Uo22C9zkeD0 Solution: http://www.youtube.com/watch
From playlist Tricks and Math Puzzles
Calculus 3: Green's Theorem (4 of 21) Applications of Green's Theorem: Ex 1A
Visit http://ilectureonline.com for more math and science lectures! In this video I will use Green's Theorem to solve the example where P=5x and Q=x^3, Ex. 1A. Next video in the series can be seen at: https://youtu.be/GfRPD4xg1wc
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM